Grayson Perry’s tapestry: ‘you could lay it out for a national picnic’. Click to see a bigger image. Photograph: National Portrait Gallery

It’s hard to define Britishness. When Gordon Brown attempted to pin down British values a decade ago it all fell a little flat: liberty and tolerance were, after all, ideals not just of Britain but of any country with a healthy respect for human rights. During the recent referendum campaign on Scottish independence, the no camp found it hard to articulate the shared characteristics and ideas that bind together the people of the union.

Can an artist do better with this slippery idea? Grayson Perry has had a stab at it in his latest tapestry, which goes on public view at the National Portrait Gallery in London on Saturday. It is a kind of portrait of a nation (“you could lay it out for a national picnic,” he says) and, like a lot of Perry’s work, teeters at the junction between earnestness and satire. The form is based on a £10 note with, of course, the Queen presiding over the image – but not depicted as the stern regal personage of our real currency, but rather as if she were “your auntie”, says Perry. “She might have stitched the whole thing in front of her hissing gas fire, with her brass ornaments twinkling in the background, Corrie playing on the telly and The Hay Wain over the fireplace.”

Perry flirts with John Major territory – “cricket on the village green” makes an appearance among Perry’s aggregation of words and phrases that seem to him to express Britishness – but it is too sly to fall for the whole warm beer and cycling spinsters schtick. Just in case you think he is getting too serious, he invokes a British quality he admires: scepticism. “Come off it!” is a phrase writ large – a warning against the notion of taking patriotism too seriously. Typically for Perry, he is sensitive to class. There is a cluster of upper-middle signifiers all in a row: “Greenbelt, nimby, green wellies, Aga, Cotswolds, M4, Eton”, and another clump of something a bit more proletarian: “boozer, red top, Blighty, allotments, Blackpool”.

Perry’s portrait of Britishness, he concedes, is at least as much about himself and his own prejudices as the nation (or nations – he doesn’t forget Wales, Scotland and Northern Ireland) he is portraying. And in the end, it is that most unfashionable of things: celebratory.

And celebratory of Britain, in particular, as a “mongrel nation”. The idea for the blanket came from talking to a friend who had arrived in Britain as a refugee from Hungary in 1956. When the plane bringing his friend in touched down, they were greeted with a recorded welcome from the Queen telling them that they had now arrived in a safe country.

His friend’s mother always thought of Britain as her “security blanket”. Perry’s ideal permanent home for the tapestry, he says, would be at a British citizenship test centre. “I like the idea of people who’ve just done the test taking selfies in front of it,” he says.

Grayson Perry: Who Are You? is at the National Portrait Gallery, London WC2, from 25 October to 15 March 2015. The Channel 4 television series of the same name begins 22 October.